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## Homework Statement

A spherical bowling ball with mass m = 4.3 kg and radius R = 0.102 m is thrown down the lane with an initial speed of v = 8.2 m/s. The coefficient of kinetic friction between the sliding ball and the ground is μ = 0.29. Once the ball begins to roll without slipping it moves with a constant velocity down the lane.

magnitude of angular acceleration during sliding: 69.66 rad/s^2

magnitude of linear acceleration during sliding: 2.84 m/s^2

how long to roll without slipping: 0.824 s

length of slide before rolling: 5.79 m

and after it begins to roll without slipping, the rotational kinetic energy is less than the translational kinetic energy.

What is the magnitude of the final velocity?

## Homework Equations

KE=1/2mv^2

Erot=1/2Iw^2

w=v/r

## The Attempt at a Solution

I assumed that the KE of the ball immediately before hitting would be equal to the sum of the final KE and Erot.

KE1=KE2+Erot

1/2mvi^2=1/2mvf^2+1/2(2/5m)(vf^2/r^2)

After mathing, I solved that the final velocity is 1.30559 m/s, but that isn't right.